Relevant bibliographies by topics / Degree of a vertex in an intuitionistic fuzzy graph

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Academic literature on the topic 'Degree of a vertex in an intuitionistic fuzzy graph'

Author: Grafiati
Published: 3 June 2025
Last updated: 22 June 2025

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Journal articles on the topic "Degree of a vertex in an intuitionistic fuzzy graph"

1

P., Karthick. "Some Classes on Product of Intuitionistic Fuzzy Graphs." Journal of Applied Mathematics and Statistical Analysis 1, no. 2 (2020): 1–8. https://doi.org/10.5281/zenodo.4067900.

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<em>Intuitionistic fuzzy graph is a generalization of a fuzzy graph. The purpose of this research paper is to calculate the degree of the vertices for an intuitionistic fuzzy graphs. This IFGs are derived from given intuitionistic fuzzy graphs based on the operators cartesian product, composition and tensor product</em>
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Yin, Songyi, Hongxu Li, and Yang Yang. "Product Operations on q-Rung Orthopair Fuzzy Graphs." Symmetry 11, no. 4 (2019): 588. http://dx.doi.org/10.3390/sym11040588.

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The q-rung orthopair fuzzy graph is an extension of intuitionistic fuzzy graph and Pythagorean fuzzy graph. In this paper, the degree and total degree of a vertex in q-rung orthopair fuzzy graphs are firstly defined. Then, some product operations on q-rung orthopair fuzzy graphs, including direct product, Cartesian product, semi-strong product, strong product, and lexicographic product, are defined. Furthermore, some theorems about the degree and total degree under these product operations are put forward and elaborated with several examples. In particular, these theorems improve the similar results in single-valued neutrosophic graphs and Pythagorean fuzzy graphs.
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Anwar, Abida, and Faryal Chaudhry. "On Certain Products of Complex Intuitionistic Fuzzy Graphs." Journal of Function Spaces 2021 (December 16, 2021): 1–9. http://dx.doi.org/10.1155/2021/6515646.

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A complex intuitionistic fuzzy set (CIFS) can be used to model problems that have both intuitionistic uncertainty and periodicity. A diagram composed of nodes connected by lines and labeled with specific information may be used to depict a wide range of real-life and physical events. Complex intuitionistic fuzzy graphs (CIFGs) are a broader type of diagram that may be used to manipulate data. In this paper, we define the key operations direct, semistrong, strong, and modular products for complex intuitionistic fuzzy graphs and look at some interesting findings. Further, the strong complex intuitionistic fuzzy graph is defined, and several significant findings are developed. Furthermore, we study the behavior of the degree of a vertex in the modular product of two complex intuitionistic fuzzy graphs.
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Parimala, Mani, Arwa Almunajam, Muthusamy Karthika, and Ibtesam Alshammari. "Pythagorean Fuzzy Digraphs and Its Application in Healthcare Center." Journal of Mathematics 2021 (September 6, 2021): 1–6. http://dx.doi.org/10.1155/2021/5459654.

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The notion of fuzzy set is introduced to deal with uncertainty, whereas the conventional sets are used for certainty. The extensions of fuzzy set theory such as intuitionistic fuzzy set (IFS) and Pythagorean fuzzy sets (PyFS) were introduced to overcome drawbacks in fuzzy theory. Fuzzy graph structure is used to deal with the uncertainty in a network and describe its relation on the nonempty vertex set. One of the extensions of intuitionistic fuzzy digraph (IFDG) is Pythagorean fuzzy digraph (PyFDG). IFDG cannot handle if the sum of degree of acceptance and degree of rejection for an arc weight exceeds 1. So, we introduced PyFDG to overcome the limitations in IFDG and it deals with the imprecise arc weight involving degree of acceptance and degree of rejection. Pythagorean fuzzy digraph (PyFDG) and its basic operations and score function of PyFDG are defined in this paper. Algorithm is proposed to solve application problem in healthcare center.
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Shoaib, Muhammad, Waqas Mahmood, Weded Albalawi, and Faria Ahmad Shami. "Notion of Complex Spherical Fuzzy Graph with Application." Journal of Function Spaces 2022 (May 18, 2022): 1–27. http://dx.doi.org/10.1155/2022/1795860.

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A complex spherical fuzzy set (CSFS) is a generalization of a spherical fuzzy set (CFS). CSFS handles vagueness more explicitly, and its range is expanded from the real subset to the complex with unit disc. The major goal of this research is to present the foundation of a complex spherical fuzzy graph (CSFG) due to the limitation of the complex neutral membership function in a complex Pythagorean fuzzy graph (CPFG). Complex spherical fuzzy models have more flexibility as compared to complex fuzzy models, complex intuitionistic fuzzy models, and complex Pythagorean fuzzy models due to their coverage in three directions: complex membership functions, neutral membership functions, and complex non-membership functions. Firstly, we present the motivation for CSFG. Furthermore, we define the order, degree of a vertex, size, and total degree of a vertex of CSFG. We elaborate on primary operations, including complement, join, and the union of CSFG. This research study introduces some operations, namely, strong product, composition, Cartesian product, and semi-strong product, on CSFG. Moreover, we present the application of CSFG, which ensures the ability to deal with problems in three directions.
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Tola, Keneni Abera, V. N. Srinivasa Rao Repalle, and Mamo Abebe Ashebo. "Theory and Application of Interval-Valued Neutrosophic Line Graphs." Journal of Mathematics 2024 (March 19, 2024): 1–17. http://dx.doi.org/10.1155/2024/5692756.

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Neutrosophic graphs are used to model inconsistent information and imprecise data about any real-life problem. It is regarded as a generalization of intuitionistic fuzzy graphs. Since interval-valued neutrosophic sets are more accurate, compatible, and flexible than single neutrosophic sets, interval-valued neutrosophic graphs (IVNGs) were defined. The interval-valued neutrosophic graph is a fundamental issue in graph theory that has wide applications in the real world. Also, problems may arise when partial ignorance exists in the datasets of membership [0, 1], and then, the concept of IVNG is crucial to represent the problems. Line graphs of neutrosophic graphs are significant due to their ability to represent and analyze uncertain or indeterminate information about edge relationships and complex networks in graphs. However, there is a research gap on the line graph of interval-valued neutrosophic graphs. In this paper, we introduce the theory of an interval-valued neutrosophic line graph (IVNLG) and its application. In line with that, some mathematical properties such as weak vertex isomorphism, weak edge isomorphism, effective edge, and other properties of IVNLGs are proposed. In addition, we defined the vertex degree of IVNLG with some properties, and by presenting several theorems and propositions, the relationship between fuzzy graph extensions and IVNLGs was explored. Finally, an overview of the algorithm used to solve the problems and the practical application of the introduced graphs were provided.
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Xiao, Wei, Arindam Dey, and Le Hoang Son. "A study on regular picture fuzzy graph with applications in communication networks." Journal of Intelligent & Fuzzy Systems 39, no. 3 (2020): 3633–45. http://dx.doi.org/10.3233/jifs-191913.

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Picture fuzzy graph (PFG) is an extended version of intuitionistic fuzzy graph (IFG) to model the uncertain real world problems, in which IFG may fail to model those problems properly. PFG is more precise, flexible and compatible than IFG to deal the real-life scenarios which consists of information these types: yes, abstain, no and refusal. The main focus of our study is to present the concept of isomorphic PFG, regular PFG (RPFG) and picture fuzzy multigraph. In this paper, we present the notation of RPFG. Many different types of RPFGs such as regular strong PFG, regular complete PFG, complete bipartite PFG and regular complement PFG are introduced. We also describe the concepts of dn and tdn-degree of a vertex in a RPFG. Based on those two types of degrees, we classify the regularity of PFG into 3 type’s namely, dn- RPFG, tdn-RPFG and n- highly irregular PFG. Several theorems of those RPFG are presented here. We define the busy vertex and free vertex in a RPFG. We present the notations of μ-complement, homomorphism, isomorphism, weak isomorphism and co weak isomorphism of RPFG. Some significant theorems on isomorphism and μ- complement of RPFG are derived here. We also introduce the notation of picture fuzzy multigraph. We present a mathematical model of communication network and transportation network by using picture fuzzy multigraph and real time data are collected so that the transportation network/communication network can work efficiently.
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Nazir, Nazia, Tanzeela Shaheen, LeSheng Jin, and Tapan Senapati. "An Improved Algorithm for Identification of Dominating Vertex Set in Intuitionistic Fuzzy Graphs." Axioms 12, no. 3 (2023): 289. http://dx.doi.org/10.3390/axioms12030289.

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In graph theory, a “dominating vertex set” is a subset of vertices in a graph such that every vertex in the graph is either a member of the subset or adjacent to a member of the subset. In other words, the vertices in the dominating set “dominate” the remaining vertices in the graph. Dominating vertex sets are important in graph theory because they can help us understand and analyze the behavior of a graph. For example, in network analysis, a set of dominant vertices may represent key nodes in a network that can influence the behavior of other nodes. Identifying dominant sets in a graph can also help in optimization problems, as it can help us find the minimum set of vertices that can control the entire graph. Now that there are theories about vagueness, it is important to define parallel ideas in vague structures, such as intuitionistic fuzzy graphs. This paper describes a better way to find dominating vertex sets (DVSs) in intuitive fuzzy graphs (IFGs). Even though there is already an algorithm for finding DVSs in IFGs, it has some problems. For example, it does not take into account the vertex volume, which has a direct effect on how DVSs are calculated. To address these limitations, we propose a new algorithm that can handle large-scale IFGs more efficiently. We show how effective and scalable the method is by comparing it to other methods and applying it to water flow. This work’s contributions can be used in many areas, such as social network analysis, transportation planning, and telecommunications.
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Myithili, K. K., and P. Nithyadevi. "Degrees and regularity of intuitionistic fuzzy semihypergraphs." Notes on Intuitionistic Fuzzy Sets 31, no. 1 (2025): 111–26. https://doi.org/10.7546/nifs.2025.31.1.111-126.

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This research work takes a new paradigm on the hypergraph concept which is a combination of a hypergraph and a semigraph. A semihypergraph is a connected hypergraph in which each hyperedge must have at least three vertices and any two hyperedges have at least one vertex in common. In a semihypergraph, vertices are classified as end, middle or middle-end vertices. This distinction, combined with membership and non-membership values, enables a more granular examination of vertices and their degrees in Intuitionistic Fuzzy Semihypergraphs (IFSHGs). This paper proposes four types of degrees: degree, end vertex degree, adjacent degree and consecutive adjacent degree on an IFSHG. Each degree reflects specific patterns within the intuitioistic fuzzy semihypergraphs. Additionally, three types of sizes are also defined: size, crisp size and pseudo size of IFSHGs. Concepts such as regular and totally regular IFSHGs with their properties are also defined.
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Isnaini Rosyida. "On Strong Fuzzy Resolving Set of Fuzzy Wheel Graphs." Advances in Nonlinear Variational Inequalities 28, no. 5s (2025): 132–39. https://doi.org/10.52783/anvi.v28.3655.

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Let Image be a fuzzy set on Image. A fuzzy labeling graph Image is a graph with bijective membership functions Image and Image so that each vertex’s membership degree and every edge’s membership value are different. Further, it satisfies Image for Image. “A graph formed from a single vertex connected to the vertices of a cycle of length Image is called a wheel graph with Image vertices". In this paper, we construct an algorithm for fuzzy labeling of wheel graphs. Under the algorithm, we have the degrees of vertices and edges are different and the monotone decreasing. The vertex Image gets the biggest degree among other vertices. Further, the edge Image is assigned to the biggest degree, and Image obtains the smallest degree. We also show the “strength of connectedness" between vertices in the fuzzy wheel graph. Finally, we investigate the “strong fuzzy resolving set" (SFRS) of the fuzzy labeling wheel graph with Image vertices and get the strong resolving number Image.
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Book chapters on the topic "Degree of a vertex in an intuitionistic fuzzy graph"

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Amanathulla, S., and Madhumangal Pal. "An Introduction to Picture Fuzzy Graph and Its Application to Select Best Routes in an Airlines Network." In Handbook of Research on Advances and Applications of Fuzzy Sets and Logic. IGI Global, 2022. http://dx.doi.org/10.4018/978-1-7998-7979-4.ch018.

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A picture fuzzy set is an extension of intuitionistic fuzzy set. In this set, a new parameter called neutral value of an object is incorporated. Based on this set, the picture fuzzy graph is defined and investigated by several scientists. Picture fuzzy graph is a new type of fuzzy graph, and it is used for solving many real life problems. In this chapter, the concept of picture fuzzy set is presented. It also introduced the picture fuzzy graph and investigated some useful properties of picture fuzzy graph. Some fundamental terms like degree of a vertex, order and size of picture fuzzy graph, strong picture fuzzy graph, complete picture fuzzy graph, independent strong and independent weak picture fuzzy edge, bipartite picture fuzzy graph, complement of a picture fuzzy graph, path, strength of a path, connectedness, homomorphism, isomorphism, automorphism, Cartesian product, composition, etc. are defined and presented some properties. An application is provided to select best airline route among multiple paths.
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Umamaheswari, K., and R. Jagajeevan. "The Role of Blockchain in Modern Libraries." In Advances in Knowledge Acquisition, Transfer, and Management. IGI Global, 2024. http://dx.doi.org/10.4018/979-8-3693-9616-2.ch007.

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This foundational approach to enhanced data management and security with special reference to TN public libraries underscores its potential to revolutionize information management and uphold the integrity of library services in the modern age. Blockchain holds immense potential in various challenges within the library domain by securely storing information in a distributed, tamper-resistant environment. Libraries unequivocally serve as catalysts for community well-being in this digital era. In intuitionistic fuzzy graphs, each vertex and edge is associated with membership and non-membership grades, reflecting the degree of blockchain belongingness and non-belongingness, respectively. The analysis and exploration of intuitionistic fuzzy graphs, particularly in the context of disjoint subgraphs and bondage sets, can lead to insights into the behavior and structure of complex systems where uncertainty and imprecision play significant roles.
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Ghorai, Ganesh, and Kavikumar Jacob. "Recent Developments on the Basics of Fuzzy Graph Theory." In Handbook of Research on Advanced Applications of Graph Theory in Modern Society. IGI Global, 2020. http://dx.doi.org/10.4018/978-1-5225-9380-5.ch018.

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In this chapter, the authors introduce some basic definitions related to fuzzy graphs like directed and undirected fuzzy graph, walk, path and circuit of a fuzzy graph, complete and strong fuzzy graph, bipartite fuzzy graph, degree of a vertex in fuzzy graphs, fuzzy subgraph, etc. These concepts are illustrated with some examples. The recently developed concepts like fuzzy planar graphs are discussed where the crossing of two edges are considered. Finally, the concepts of fuzzy threshold graphs and fuzzy competitions graphs are also given as a generalization of threshold and competition graphs.
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Naga Srinivasa Rao Repalle, Venkata, Keneni Abera Tola, and Maamo Abebe Ashebo. "Extended Intuitionistic Fuzzy Line Graphs: Theory and Properties." In Coding Theory Essentials [Working Title]. IntechOpen, 2023. http://dx.doi.org/10.5772/intechopen.110182.

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The introduction of fuzzy set theory was given by Zadeh. The introduction of fuzzy graph theory was given by Kauffman. Later the structure of fuzzy graph was developed Rosenfeld. The traditional fuzzy set cannot be used to completely describe all the evidence in problems where someone wants to know in how much degree of non-membership. Such a problem got the solution by Atanassov who introduced intuitionistic fuzzy set which described by a membership, a non-membership and a hesitation functions. An intuitionistic fuzzy set is used to solve problems involving uncertainty and imprecision that can’t be handled by a traditional fuzzy set. This chapter introduced the interval-valued intuitionistic fuzzy line graphs (IVIFLG) and explored the results related to IVIFLG. As a result, many theorems and propositions related to IVIFLG are developed and supported by proof. Moreover, some remarkable isomorphic properties, strong IVIFLG, and complete IVIFLG have been investigated, and the proposed concepts are illustrated with the examples.
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Pillai, Nagarajan Deivanayagam, Lathamaheswari Malayalan, Said Broumi, Florentin Smarandache, and Kavikumar Jacob. "New Algorithms for Hamiltonian Cycle Under Interval Neutrosophic Environment." In Advances in Data Mining and Database Management. IGI Global, 2020. http://dx.doi.org/10.4018/978-1-7998-1313-2.ch004.

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A cycle passing through all the vertices exactly once in a graph is a Hamiltonian cycle (HC). In the field of network system, HC plays a vital role as it covers all the vertices in the system. If uncertainty exists on the vertices and edges, then that can be solved by considering fuzzy Hamiltonian cycle. Further, if indeterminacy also exist, then that issue can be dealt efficiently by having neutrosophic Hamiltonian cycle. In computer science applications, objects may not be a crisp one as it has uncertainty and indeterminacy in nature. Hence, new algorithms have been designed to find interval neutrosophic Hamiltonian cycle using adjacency matrix and the minimum degree of a vertex. This chapter also applied the proposed concept in a network system.
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